Abstract

This thesis deals with the Boyd-Barratt paradigm for feedback controller design. The Boyd-Barratt approach combines the Youla parameterization with convex optimization. In this thesis, their paradigm is accepted in its entirety, but a completely different numerical approach is adopted. An algorithm due to Akilov and Rubinov, which is in essence an abstract rendition of one of the famous algorithms of Remez, is used instead. This completely circumvents the need to compute derivatives or subdifferentials, which can be a difficult task. Instead, certain linear functionals must be computed, and this is generally quite straightforward. An attractive feature of the approach is that the code is much shorter and more elegant. The Boyd-Barratt paradigm has the disadvantage that an infinite dimensional Banach space must be truncated to a finite dimensional subspace prior to optimizing. This thesis also applies certain primal-dual techniques from functional analysis to study the implications of this truncation. Primal-dual theory is used to show th a t the true optimal solution lies within the solution of two semi-infinite linear programming problems, namely the dual problem with finitely many variables and the primal problem with finitely many variables. Also, it is shown th a t the alignment property is closely related to the cost of truncation. These results provide an analysis of the effect of truncation.